The mating or insertion of a rod or peg with a hole is a common industrial task which people perform with ease and machines perform with difficulty. If either the peg or the hole are bevelled or chamfered the task is easier but if there is no chamfer the need for precise alignment makes it quite difficult. The necessary alignment precision may be too costly to achieve, making automation of such operations impractical. An insertion with chamfers has the same difficulty and geometric description as one without chamfers if the initial lateral misalignment between peg and hole is much larger than the chamfer. Two classes of devices which ease automated chamfered insertion are the remote center compliance device (RCC), see U.S. Pat. Nos. 4,098,001 and 4,155,169; and the Hi-Ti-Hand. See U.S. Pat. Nos. 3,824,674 and 3,984,006. The RCC alone has not yet achieved chamferless insertion. The Hi-Ti-Hand can perform chamferless insertion as well, but it does so slowly. Also, it is a complex electromechanical device.